Geodesic
On Wiener's attack on RSA cryptosystem
Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 189-194.

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We propose a modification of Wiener’s attack on the RSA cryptosystem. The algorithm uses only continuous fractions. It's complexity is not greater than $O(d^2 m^{-1/2} \ln m)$, where $m$ is the modulus, $d$ is the secret exponent of RSA. 
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A. A. Illarionov; S. A. Chepurko. On Wiener's attack on  RSA cryptosystem. Dalʹnevostočnyj matematičeskij žurnal, Tome 18 (2018) no. 2, pp. 189-194. http://geodesic.mathdoc.fr/item/DVMG_2018_18_2_a5/

[1] R. L. Rivest, A. Shamir, L. Adleman, “A method for obtaining digital signatures and publi-key cryptosystems”, Communications of the ACM, 21 (1978), 120–126 | DOI | MR | Zbl

[2] M.,J. Wiener, “Cryptanalysis of short RSA secret exponents”, IEEE Trans. Inform. Theory, 36 (1990), 553–558 | DOI | MR | Zbl

[3] E. R. Verheul, H. C. A. van Tilborg, “Cryptanalysis of “less short” RSA secret exponents”, Appl. Algebra Engrg. Comm. Computing, 8 (1997), 425–435 | DOI | MR | Zbl

[4] A. Dujella, “Continued fractions and RSA with small secret exponent”, Tatra Mt. Math. Publ., 29 (2004), 101–112 | MR | Zbl

[5] A. Dujella, “A variant of Wiener's attack on RSA”, Computing, 85 (2009), 77–83 | DOI | MR | Zbl

[6] D. Boneh and G. Durfee, “Cryptanalysis of RSA with private key $d$ less than $0.292$”, in Advances in Cryptology-EUROCRYPT '99, Lecture Notes in Computer Science, v. 1592, Springer, Berlin, Germany, 1999, 1–11 | MR | Zbl

[7] J. Blomer, A. May, “Low secret exponent RSA revisited”, Cryptography and Lattice - Proceedings of CaLC 2001, Lecture Notes in Comput. Sci., v. 2146, 2001, 4–19 | MR | Zbl